1884.] of the electromagnetic field. 147 



of the given wave of magnetic force. For' the present we will 

 omit it and put 



, AX (Ll + Mm + Nn) * /£> ^ N 



3> = - w-^r- 77— L cosS (27), 



and then we have 



Thus from (9) 



4f7rV sine 





V 2 ®=-^ (28), 



and © = j- - III - dx'dy'dz = %. 



This quantity ^ disappears from the expressions for the displace- 

 ment, and according to Maxwell (Electricity and Magnetism, 11.) 

 is not connected with any known Physical Phenomenon. He 

 therefore neglects it. More strictly, according to Helmholtz, it 

 may be needed to express completely the action of an element of 

 current at a distant point, and he shews reason for putting 



d® 

 J= ~ flk -dt> 

 k being an indeterminate constant, and then we have 



and hence <| = - ^l^^l^dx'dy'dz . 



d'v 



We can easily in the case before us evaluate --A , 



and we find 



djt = jiAXl _ „ „ L + mM+ ™ cog s> 



dx 2tt sin e 



and hence for the complete value of F 



F=- f AX \L-l(l-k) (IL + mM+ nN) cos S. 

 27rsine l 



Thus on this theory F is a vector travelling at the same rate as 

 a, ft, 7, but its direction depends on the value of k. 



In the general case in which the unknown quantity % is re- 

 tained F may be divided into two parts, the one travels with the 

 velocity V, and has for direction cosines L, M, N, that is it lies in a 

 plane through the wave normal and at right angles to the magnetic 

 force, the other is normal to the surface % = constant, but its rate 

 of motion is unknown. The direction cosines of f, g, h are also 



10—2 



